T. Si, \. T. , and \. , T n est un k-simplexe (k < 3) qui intersecte T alors Bd p T est connexe. preuve : Supposons que T 1 \ T 2 \ :::T n soit un k-simplexe (k < 3) qui intersecte T. Soit a = ( T 1 \T 2 \:::T n ) \T le k-simplexe qui est l

T. Or and \. , Donc (T i \ T) est une r eunion de k-simplexes qui contiennent t o u s a ce qui entra^ ne que Bd p T = (T i \ T)

A. Aktouf, G. Bertrand, and E. L. Perroton, A 3D-hole closing algorithm, Proceedings of DGCI'96, pp.36-48, 1996.
DOI : 10.1007/3-540-62005-2_4

A. Arun, T. Huang, and E. S. Blodstein, Least-square Fitting of two 3D points, I E E E T ransactions on Pattern Analysis and Machine Intelligence, pp.207-209, 1987.

S. Baillet, Vers une imagerie fonctionnelle de l' el ectrophysiologie corticale. Mod elisation markovienne pour l'estimation des sources de l' electro/magn etoenc ephalographie et evaluations exp erimentales, T h ese de doctorat, pp.1998-5353

B. Bertrand and G. Malandain, A New Characterization of Three-dimensional Simple Points, P attern Recognition Letters, pp.169-175, 1994.

B. Bertrand, Simple points, topological numbers and geodesic neighbourhoods in cubic grids, P attern Recognition Letters, pp.1003-1011, 1994.

B. Besl and N. M. Kay, A m e t h o d for registration of 3D- shapes, I E E E T ransactions on Pattern Analysis and Machine Intelligence, pp.239-256, 1992.

I. Bloch, H. Ma^-tre, and E. M. Minoux, Optimal Matching of 3-D Convex Polyhedra with Applications to Pattern Recognition , P attern Recognition and Image Analysis, pp.137-149, 1993.

B. George and H. Borouchaki, Triangulation de Delaunay : Application aux el ements nis, Hermes, 1999.

B. Borgefors, An improved version of the chamfer matching algorithm, 7th International Conference on Pattern Recognition Distance t r ansformations in digital images, Computer Vision, Graphics, and Image Processing 344{ 371. BOW-81] A. Bowyer, Computing Dirichlet tessellations, pp.24-162, 1981.

J. Cavendish, D. Field, and E. W. Frey, An apporach to automatic three-dimensional finite element mesh generation, International Journal for Numerical Methods in Engineering, vol.3, issue.2, pp.329-347, 1985.
DOI : 10.1002/nme.1620210210

C. Cendes, D. Shenton, and E. H. Shanhaser, Magnetic eld computations using Delaunay triangulations and complementary nite element methods, I, E.E.E. Transactions Magnetics, vol.21, 1985.

C. Ciarlet, Basic Error Estimates for Elliptic Problems, in Handbook of Numerical Analysis, vol II, Finite Element methods, 1991.

I. Cointepas, E. L. Bloch, and . Garnero, A cellular model for multi-objects multi-dimensional homotopic deformations, Pattern Recognition, vol.34, issue.9, pp.1785-1798, 2001.
DOI : 10.1016/S0031-3203(00)00106-0

E. E. Et and M. E. Ese-de-doctorat, Cointepas, Mod elisation homotopique et segmentation 3D du cortex c er ebral a p artir d'I.R.M. pour la r esolution des probl emes direct et inverse en, Ecole Nationale Sup erieure des T el ecommunications, 1999.

D. Dale and M. Sereno, Improved l o calization of cortical activity by combining EEG and MEG with MRI cortical surface r econstruction: a linear approach, Journal of Cognitive Sciences, vol.5, pp.162-176, 1993.

D. Delaunay, Sur la sph ere vide, Bulletin de l'Acad emie des Sciences, pp.793-800, 1934.

D. Dirichlet, Uber die Reduction Der positiven quadratishen Formen mit drei understimmenten ganzen Zahlen, Z. Angew Math. Mech, vol.40, pp.209-227, 1850.

P. Van-den-elsen, M. Viergever, A. Van-huffelen, W. Van-der-meu, and E. G. Weineke, Accurate Matching of electromagnetic dipole data with CT and MR images, Brain Topography, vol.85, issue.Suppl. 133, pp.425-432, 1991.
DOI : 10.1007/BF01129001

O. Faugeras, Three-Dimensional Computer Vision, 1993.

F. Frey and P. George, Maillages : Application aux m ethodes d' el ements nis, Hermes, 1999.

F. Fuchs, Optimierung von Delaunay-Triangulierungen, Th ese de doctorat, 1996.

G. Gavit, S. Baillet, J. Pescatore, and E. L. Garnero, M ethode multir esolution en tomographie electrique c er ebrale: application a l a r econstruction de la repr esentation corticale de la main en magn etoenc ephalographie, ITBM-RBM, p.22, 2001.

G. Geddes and L. Becker, The specific resistance of biological material???A compendium of data for the biomedical engineer and physiologist, Medical & Biological Engineering, vol.5, issue.3, pp.271-293, 1967.
DOI : 10.1007/BF02474537

G. George, Computer implementation of the nite element method

B. G. Gera-98-]-t and . Eraud, Segmentation des structures internes du cerveau en imagerie par r esonance magn etique tridimensionnelle, Th ese de doctorat, Ecole Nationale Sup erieure des T el ecommunications

G. Gevins, Dynamic functional topography of cognitive tasks, Brain Topography, vol.59, issue.2, pp.37-56, 1989.
DOI : 10.1007/BF01128842

G. Gordon and C. Hall, Construction of curvilinear coordinate systems and application to mesh generation, I n ternational, Journal of Numerical Methods In Engineering, pp.7-461, 1973.

G. Green and R. Sibson, Computing Dirichlet Tessellations in the Plane, The Computer Journal, vol.21, issue.2, pp.168-173, 1978.
DOI : 10.1093/comjnl/21.2.168

E. Ransactions-on, Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data, I, J. Sarvas Biomedical Engineering, pp.36-165, 1989.

H. , R. Hari, R. J. Ilmoniemi, J. Knuutila, O. V. Lounasmaa et al., Instrumentation and Applications to Non-invasive Studies of the Working Human Brain, Reviews of Modern Physics, pp.65-413, 1993.

H. Haueisen, M. Eiselt, C. Ramon, E. H. Brauer, and . Nowak, Innuence of tissue resistivities on neuromagnetic elds and electric potentials studied with a nite element model of the head, IEEE Transactions on Biomedical Engineering, pp.44-727, 1997.

H. T. Herman, On topology as applied to image analysis, Computer Vision, Graphics, and Image Processing, pp.52-409, 1990.

H. Hermeline, Une m ethode de maillage en dimension n, Th ese de doctorat, 1980.

R. Hosek, A. Sances, R. Jodat, S. Larson, E. E. Evoked-p-otentials et al., The contributions of intracerebral currents to the, Biomedical Engineering, pp.25-728, 1978.

K. Kahle, H. Leonhardt, and E. W. Platzer, Anatomie 3 -S y s t eme nerveux, Flammarion-M edecine-Sciences, 1990.

K. Y. Kong, ON TOPOLOGY PRESERVATION IN 2-D AND 3-D THINNING, International Journal of Pattern Recognition and Artificial Intelligence, vol.09, issue.05, pp.813-844, 1995.
DOI : 10.1142/S0218001495000341

K. A. Kovalevsky, Finite Topology as Applied to Image Analysis, Computer Vision, Graphics, and Image Processing, pp.141-146, 1989.

C. Lee, T. Poston, and E. A. Rozenfeld, Holes and Genus of 2D and 3D Digital Images, Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing, A new mesh generation sheme for arbitrary planar domain, I n ternational, Journal of Numerical Methods in Engineering, vol.55, pp.63-141, 1985.

R. L. Ohner, Extensions and improvements of the advancing front grid generation technique, C o m m unication of Numerical Methods in Engineering, pp.683-702, 1996.

M. Mangin, Mise en correspondance d'images m edicales 3D multi-modalit es multi-individus pour la corr elation BIBLIOGRAPHIE anatomo-fonctionnelle c er ebrale, T h ese de doctorat, Ecole Nationale Sup erieure des T el ecommunications

M. Mangin, O. Coulon, and E. V. Frouin, Robust brain segmentation using histogram scale-space analysis and mathematical morphology, Medical Image Computing and Computer Assisted Intervention (MICCAI'98), pp.1230-1241, 1998.
DOI : 10.1109/34.19041

G. Marin, C. Gu-erin, S. Baillet, and E. L. Garnero, Influence of skull anisotropy for the forward and inverse problem in EEG: Simulation studies using FEM on realistic head models, Human Brain Mapping, vol.21, issue.4, pp.250-269, 1998.
DOI : 10.1002/(SICI)1097-0193(1998)6:4<250::AID-HBM5>3.0.CO;2-2

M. P. Meijs, O. Weier, and A. Oosteron, On the numerical accuracy of the boundary element method (EEG application), IEEE Transactions on Biomedical Engineering, vol.36, issue.10, pp.1038-1049, 1989.
DOI : 10.1109/10.40805

M. Minoux, Programmation Math ematiques : th eorie et algorithmes, 1983.

M. G. Morgenthaler, Three dimensional simple points : serial erosion, parallel thinning, and skeletonization, 1981.

M. D. Munck, The potential distribution in a layered anisotropic spheroidal volume conductor, Journal of Applied Physics, vol.64, issue.2, pp.464-470, 1988.
DOI : 10.1063/1.341983

N. Nicholson, Speciic impedance o f c erebral white matter, Experimental Neurophysiology, vol.13, pp.386-396, 1965.

N. Nikou, J. Armspach, F. Heitz, I. Namer, E. D. Grucker et al., Registration of MR/MR and MR/SPECT Brain Images by Fast Stochastic Optimization of Robust Voxel Similarity Measures, NeuroImage, vol.8, issue.1, pp.8-30, 1998.
DOI : 10.1006/nimg.1998.0335

H. Rifai, I. Bloch, S. Hutchinson, J. Wiart, and E. L. Garnero, Segmentation of the skull in MRI volumes using deformable model and taking the partial volume effect into account, Medical Image Analysis, vol.4, issue.3, pp.219-233, 2000.
DOI : 10.1016/S1361-8415(00)00016-5

M. Rivara and C. Levin, A 3 d r eenement algorithm suitable for adaptive and multigrid techniques, Journal of Computing and applied Mathematics, vol.8, pp.281-290, 1992.

M. Rivara, New longest-edge algorithms for the reenement and/or improvement of unstructured triangulations, I n ternational journal on numerical methods in engineering, pp.3313-3324, 1997.

R. Robillard and Y. Poussart, Speciic impedance m e asurements of brain tissues, Medicine and Bioengineering, vol.15, pp.438-445, 1977.

R. Rush and D. Driscoll, Current distribution in the brain from surface electrodes, Anesthesia and analgesia, current researches, pp.47-717, 1968.

S. Saha and A. Rosenfeld, Determining simplicity and computing topological change in strongly normal partial tilings of R2 or R3, P attern Recognition, pp.105-118, 2000.

S. K. Saha, B. Chanda, and D. D. Majumder, Principles and algorithms for 2-D and 3-D shrinking, 1991.

S. Saha and D. D. Majumber, Local Topological Parameters in a, Tetrahedral Representations Graphical Models and Image Processing, pp.60-423, 1998.

S. Saha and A. Rosenfeld, Strongly normal sets of convex polygons or polyhedra, Pattern Recognition Letters, vol.19, issue.12, pp.1119-1124, 1998.
DOI : 10.1016/S0167-8655(98)00088-9

S. Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem, Physics in Medicine and Biology, vol.32, issue.1, pp.11-22, 1987.
DOI : 10.1088/0031-9155/32/1/004

M. Scherg, D. V. Et, and . Cramon, Evoked dipole source potentials of the human auditory cortex, Electroencephalography and Clinical Neurophysiology/Evoked Potentials Section, vol.65, issue.5, pp.344-360, 1986.
DOI : 10.1016/0168-5597(86)90014-6

M. E. Et and E. E. Ese-de-doctorat, Localisation des g en erateurs intra-c er ebraux de l'activit, 1998.

S. Shephard, F. Guerinoni, J. Flaherty, R. Ludwig, and E. P. Baehman, Adaptive solutions of the Euler equations using nite quatree a n d o ctree grids, Computers and Structures, pp.30-327, 1988.

S. Sheynin and A. Tuzikov, Explicit formulae for polyhedra moments, P attern Recognition Letters, pp.1103-1109, 2001.

S. Singh, I. Holliday, P. Furlong, and E. G. Harding, Evaluation of MRI-MEG/EEG co-registration strategies using Monte-Carlo simulation, Electroencephalography clinical neurophysiologie, pp.81-85, 1997.

S. Swartz and E. Goldensohn, Timeline of the history of EEG and associated elds, Electroencephalography Clinical Neurophysiology, vol.34, pp.173-176, 1998.

T. Thompson, Z. Warsi, and C. Mastin, Numerical grids generation, foundation and applications, 1985.

B. Thom-93-]-r and . Thompson, The bra i n -A N e u r oscience primer, F reeman and Co, 1985.

T. I. Toriwaki, S. Yokoi, T. Yonekura, and E. T. Fukumura, Topological properties and topology-preserving transformation of a three-dimensional binary picture, 6th International Conference on Pattern Recognition, pp.414-419, 1989.

T. F. Tsao-e-t and K. S. , A parallel thinning algorithm for 3-D pictures, Computer Graphics and Image Processing, vol.17, issue.4, pp.315-331, 1981.
DOI : 10.1016/0146-664X(81)90011-3

W. F. Watson, Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes, The Computer Journal, vol.24, issue.2, pp.167-172, 1981.
DOI : 10.1093/comjnl/24.2.167

W. Wells, R. Kikinis, and E. F. Jolesz, Adaptive segmentation of MRI data, IEEE Transactions on Medical Imaging, vol.15, issue.4, pp.429-442, 1996.
DOI : 10.1109/42.511747

Y. Yamamoto and Y. Yamamoto, Electrical properties of the epidermal stratum corneum, Medical & Biological Engineering, vol.205, issue.2, 1976.
DOI : 10.1007/BF02478741

L. Dii-erents-sch-emas and .. , H11 a H16) de subdivision autour d'un sommet

.. Les-dii-erents-sch-emas, H21 a H24) de subdivision autour de deux sommets, pp.2-3

L. Dii-erentes-niveaux-de-subdivision-d-'une and T. , P:R:des tissus de la t^ ete

.. , T. F. Pour-le-calcul-d-'un-moment-g-eom-etrique, and .. , T etra edres simples de l' etiquetage homotopique (en noir) superpos es a la segmentation des tissus de la t^ e t e, p.157

. Scalp and . Cerveau, superposition de la segmentation (en fonn c e) et du maillage homotopique t etra edrique (en clair) pour la r esolution (n = 3) de la T, P.R, vol.1, issue.5, p.9

. Scalp and . Cerveau, superposition de la segmentation (en fonn c e) et du maillage homotopique t etra edrique (en clair) pour la r esolution (n = 4) de la T, P.R, vol.1, issue.5, p.9

V. Etude-du-param-etre and . Pour, Superposition des t etra edres simples du cr^ ane (en noir) avec la segmentation, pp.6-6

V. Etude-du-param-etre and . Pour, Superposition des t etra edres simples de la t^ ete (en noir) avec la segmentation, pp.6-7

T. Histogrammes-d-'une, (a) qualit e Q ;1 , (b) qualit e Q , (c) longeurs d'ar^ etes e, 0175.

T. Histogrammes-d-'une, P:R: adapt ee correspondant t a l'union des tissus de la t^ ete. (a) qualit e Q, p.176

T. Erreur-relative-e-m=m-v-=-jm, P:R ; M voxels j =M voxels des moments d'ordre 2 pour des T:P:R: de r esolution 3 et 4 par rapport a la segmentation, du cerveau, vol.1, p.8

M. Erreur-relative-e, =. , and T. , P:R ; M voxels j =M voxels des moments jusqu'' a l'ordre 2 des T:P:R: de r esolution 3 et 4 par rapport a la segmentation du cr^ ane, p.160

T. Erreur-relative-e-m=m-v-=-jm, P:R ; M voxels j =M voxels des moments jusqu'' a l'ordre 2 pour des T:P:R: de r esolution 3 et 4 par rapport a la segmentation de la t^ ete, ., vol.1, issue.6, p.0

N. Nombre-de-t-etra-edres and T. Tetra-et-d-'ar^-etes-n-a-des, P:R:adapt ees pour les dii erents objets maill e s, 0171.

T. Longueur-e-d-'ar^-ete-d-'une, P:R: adapt ee pour les dii erents tissus maill e s, 0174.

T. Qualit-e-q-d-'une, P:R: adapt ee pour les dii erents tissus maill e s, 0174.